\chapter{Introduction}
\label{chapter:intro}

The process of diffusion is the spread of information or some flow in
a network through local transmissions. Many real world applications
can be modeled as diffusion processes over networks. Some prominent
examples include diseases transmitted among humans, viruses
transmitted over computer networks, information/ideas spreading over
contact networks, and creation of friendships through social
networks. Despite the diversity among these applications, there are
fundamental similarities in the mathematical models. Understanding the
properties of these applications through mathematical models can help
us anticipate, exploit, and control the propagation processes.

Based on the information or nature of the commodity that is flowing,
we classify diffusion processes into the following two categories,
{\em positive diffusion} and {\em negative/harmful diffusion}. In
positive diffusion, the information or commodities are useful to the
nodes, like innovation and ideas, whereas in negative diffusion, the
information or commodities are harmful to the nodes, like diseases and
viruses. In positive diffusion, we are interested in analyzing the
converging time and designing efficient algorithms for fast
diffusion. While in negative diffusion, we are interested in analyzing
the converging time and the extent of diffusion processes, as well as
designing good intervention strategies. Take the spread of a disease
or computer virus as an example.  Lots of important questions can be
asked. Will it become an epidemic? How much time does it take to
become an epidemic? Who will get infected? What's the social cost of
the epidemic? Once we understand all these, we can design
interventions to control the dynamics. For instance, how do we
vaccinate or quarantine the population so that the epidemic is
controlled? How do we secure computers to enhance the network
resilience? What polices should be applied with budget constraints
(limited vaccines or anti-virus software licenses), how should we
distribute resources, and how much can we reduce social cost?  Often
these interventions can be translated into voluntary directives from
government, like take vaccines or stay at home. However, people
usually don't adhere to such recommendations. Instead, they make
decisions based on their specific utilities and objectives. Such
decisions happen in a decentralized manner, which makes game theory a
natural approach to study these problems. Moreover, people alter their
contacts dynamically. For example, a vaccinated person may increase
his/her contacts with friends, due to perceived secure feelings. These
behavioral changes have a huge impact on the dynamics and the
effectiveness of these interventions, so that ``good'' intervention
strategies might be ineffective, depending on the behavioral
changes. All these make the analysis of diffusion processes more
interesting and challenging.

In the first half of this dissertation, we concentrate on enabling
positive diffusion. More interestingly, we focus on the diffusion
processes on dynamically changing networks. The networks can be
changed by the diffusion process itself or by an adversary. We
introduce the problems in these two types of dynamic networks in
detail in Section~\ref{sec:intro.discovery} and
Section~\ref{sec:intro.token} respectively. In the second half of this
dissertation, we switch gear to controlling negative diffusion. We
design both centralized and decentralized strategies to control
negative diffusion, introduced in Section~\ref{sec:intro.game}. We
further consider the effects of individual behavior changes on the
design of control strategies, which is introduced in
Section~\ref{sec:intro.risk}.

\input{1_introduction/discover_intro}
\input{1_introduction/token_intro}
\input{1_introduction/game_intro}
\input{1_introduction/risk_intro}
\input{1_introduction/outline}

